This paper examines the implications of the seasonal adjustment by an ARIMA
model based (AMB) approach in the context of seasonal fractional integration.
According to the AMB approach, if the model identified from the data contains seasonal
unit roots, the adjusted series will not be invertible that has serious implications for the
posterior analysis. We show that even if the ARIMA model identified from the data
contains seasonal unit roots, if the true data generating process is stationary seasonally
fractionally integrated (as it is often found in economic data), the AMB seasonal
adjustment produces dips in the periodogram at seasonal frequencies, but the adjusted
series still can be approximated by an invertible process. We also perform a small
Monte Carlo study of the log-periodogram regression with tapered data for negative
seasonal fractional integration. An empirical application for the Spanish economy that
illustrates our results is also carried out at the end of the article.
JEL Classification: C15.
Keywords: seasonality; invertibility; fractional integration; TRAMO-Seats; tapering